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We present a novel methodological framework for quantum spatial search, generalising the Childs & Goldstone ($\mathcal{CG}$) algorithm via alternating applications of marked-vertex phase shifts and continuous-time quantum walks. We…

Quantum Physics · Physics 2021-09-30 S. Marsh , J. B. Wang

A powerful strategy to accelerate quantum-walk-based search algorithms leverages on resetting protocols, where a detector monitors a target site and the evolution of the walker is restarted if no detection occurs within a fixed time…

Quantum Physics · Physics 2025-11-03 Sayan Roy , Shamik Gupta , Giovanna Morigi

Quantum walk is fundamental to designing many quantum algorithms. Here we consider the effects of quantum coherence and quantum entanglement for the quantum walk search on the complete bipartite graph. First, we numerically show the…

Quantum Physics · Physics 2023-10-03 Meng Li , Xian Shi

Quantum algorithms have demonstrated provable speedups over classical counterparts, yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge. In this work, we decode the quantum…

Quantum Physics · Physics 2025-11-11 Si-Qi Zhou , Jin-Min Liang , Ziheng Ding , Zhihua Chen , Shao-Ming Fei , Zhihao Ma

Let $X$ be a graph with adjacency matrix $A$. The \textsl{continuous quantum walk} on $X$ is determined by the unitary matrices $U(t)=\exp(itA)$. If $X$ is the complete graph $K_n$ and $a\in V(X)$, then \[1-|U(t)_{a,a}|\le2/n. \] In a…

Combinatorics · Mathematics 2017-11-01 Chris Godsil

Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…

In this paper, we study the impact of single extra link on the coherent dynamics modeled by continuous-time quantum walks. For this purpose, we consider the continuous-time quantum walk on the cycle with an additional link. We find that the…

Mathematical Physics · Physics 2012-05-01 Xin-Ping Xu , Yusuke Ide , Norio Konno

Consider a nearest neighbor random walk on the two-dimensional integer lattice, where each vertex is initially labeled either `H' or `V', uniformly and independently. At each discrete time step, the walker resamples the label at its current…

Probability · Mathematics 2023-05-11 Swee Hong Chan

Quantum walks can be used either as tools for quantum algorithm development or as entanglement generators, potentially useful to test quantum hardware. We present a novel algorithm based on a discrete Hadamard quantum walk on a line with…

Quantum Physics · Physics 2009-01-27 Salvador E. Venegas-Andraca , Sougato Bose

Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of…

Quantum Physics · Physics 2021-01-04 Tong Wu , J. A. Izaac , Zi-Xi Li , Kai Wang , Zhao-Zhong Chen , Shining Zhu , J. B. Wang , Xiao-Song Ma

We give new observations on the mixing dynamics of a continuous-time quantum walk on circulants and their bunkbed extensions. These bunkbeds are defined through two standard graph operators: the join G + H and the Cartesian product of…

Quantum Physics · Physics 2014-11-18 P. Lo , S. Rajaram , D. Schepens , D. Sullivan , C. Tamon , J. Ward

Continuous-time quantum walks (CTQW) have shown the capability to perform efficiently the spatial search of a marked site on many kinds of graphs. However, most of such graphs are hard to realize in an experimental setting. Here we study…

Quantum Physics · Physics 2021-12-08 C. Benedetti , D. Tamascelli , M. G. A. Paris , A. Crespi

We introduce the concept of a quantum walk with two particles and study it for the case of a discrete time walk on a line. A quantum walk with more than one particle may contain entanglement, thus offering a resource unavailable in the…

Quantum Physics · Physics 2007-05-23 Y. Omar , N. Paunkovic , L. Sheridan , S. Bose

We develop a new framework that extends the quantum walk framework of Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data structures to construct an efficient method of nesting quantum walks. Surprisingly, only…

Quantum Physics · Physics 2016-05-24 Stacey Jeffery , Robin Kothari , Frederic Magniez

Simulation and programming of current quantum computers as Noisy Intermediate-Scale Quantum (NISQ) devices represent a hot topic at the border of current physical and information sciences. The quantum walk process represents a basic…

We study search by quantum walk on a finite two dimensional grid. The algorithm of Ambainis, Kempe, Rivosh (quant-ph/0402107) takes O(\sqrt{N log N}) steps and finds a marked location with probability O(1/log N) for grid of size \sqrt{N} *…

Quantum Physics · Physics 2011-12-15 Andris Ambainis , Arturs Backurs , Nikolajs Nahimovs , Raitis Ozols , Alexander Rivosh

Fast computational algorithms are in constant demand, and their development has been driven by advances such as quantum speedup and classical acceleration. This paper intends to study search algorithms based on quantum walks in quantum…

Quantum Physics · Physics 2026-01-06 Yazhen Wang

With photonics, the quantum computational advantage has been demonstrated on the task of boson sampling. Next, developing quantum-enhanced approaches for practical problems becomes one of the top priorities for photonic systems. Quantum…

Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms…

Quantum Physics · Physics 2015-05-19 Birgit Hein , Gregor Tanner

Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…

Quantum Physics · Physics 2019-12-18 Alexey A. Melnikov , Leonid E. Fedichkin , Alexander Alodjants